We are in the minority but we were "meh" about Diamond Head. Glad we did it, but it was harder than we were expecting considering what a big tourist destination it is. We are in our early 30s, average shape and found parts difficult. Lots of stairs, uphill (obviously), and uneven terrain. The trail also gets crowded later in the day and there is little room to pull over and rest, so its tough to go at your own pace. It's a conga line of people in front of you and behind you. With 6 kids, you need to trust they will keep up and stay together. When we got to the top, the views were beautiful but it was very crowded and very windy. Another con for us is that we were very sweaty and gross afterward as most of the trail is in direct sun so it gets hot. We needed to go back to our hotel to shower and change before we could do anything else that day.
If you decide to go for it, I echo the PPs recommendation of going as early as possible both for the parking and the heat, and also because the trail will be less crowded earlier in the day.
The North Shore, on the other hand, was one of our favorite places. We drove ourselves because we had a car which gave us the flexibility to explore. We did Dole which was ok, likely more fun for kids. Highly recommend stopping at Matsumoto's for shave ice!